Question

A simple pendulum has a hallow bob filled with a liquid of density p. If the liquid drains out of a small hole in the bottom of the bob, then frequency of oscillations:

• A. goes on increasing
• B. goes on decreasing
• C. remains same
• D. first increases and then decreases

Answer 1

Answer: (B)

goes on decreasing

$\begin{array}{c}\text{A Bob with density}\left(\rho \right)\text{liquid}\\ \text{The liquid drains out the Bob.}\end{array}$

$\text{we have}[\nu =\frac{1}{2\pi }\cdot \sqrt{\frac{g}{e}}]$

$\begin{array}{c}\text{with liquid filled Bob}\\ \text{as the liquid drains out the level of the}\\ \text{liquid decreases and hence the COM}\\ \text{(centre of Mass) of the Bob also lowers}\\ \text{This means (l) length increases.}\end{array}$

$\begin{array}{c}\text{Now from the relation - (1)}\\ \text{as}\ell \text{increases then}v\text{decreases}\\ \Rightarrow \text{Frequency of oscillation decreases.}\end{array}$